This is a great question, and fortunately for me, it's a pretty easy one to answer! I have written another comment right here that brings up some similar themes to what I'll write below, if you feel like checking that one out or reading more.
I'm procrastinating on grading final exams and dealing with my flooded email inbox, so I'm open to follow-up questions on this one for a while. If I don't get to it today, I'll try my best to get to it later.
All crime rates spiked from the late 70s through the early 90s. Serial killings were no exception. They were, and are, exceedingly rare, despite receiving excessive media attention. The answer to the question of why serial killings spiked in the 70s-90s is no more readily available than the answer to the question of why crime spiked in the 70s-90s, unfortunately.
I broke this down into three comments. References are linked in the comments in a few places, but my big list of references cited are in Part 3.
Part 1: Crime rates as a whole spiked from the 70s through the early 90s.
Part 2: Criminologists don't really know why crime rates spiked during this time period.
Part 3: Criminologists REALLY don't know why serial killers act at all, but we can (probably) use the same logic behind the other theories of crime rates to try to understand serial killers.
First and foremost, you should know that serial killers were, and are, exceedingly rare. For instance, Sturup (2018) notes that less than 2% of all homicides can be attributed to serial homicide offenders. Their literature review is worth the read, as it includes citations from several different countries (including Sweden, the U.S., and England), and surveys literature that studies the time period you specified (70s through 90s).
More to your question, all crime spiked from the late 70s through the early 90s. In fact, the crime rate started slowly creeping up right after WWII, spiked way up around the 1980s, and just didn't stop until the mid-90s (at which point it plummeted and it mostly continues to drop today). This includes both violent and nonviolent crime. The FBI's Crime Data Explorer (CDE) is freely available online and is pretty easy to use. The CDE is a compilation of police report data from 1985 to 2020 (and 2021 data will probably be available by mid-2022), as part of the Uniform Crime Report (UCR) program (read more on the FBI's website). It does not include data from before 1985 because of how the UCR works - police agencies voluntarily report into the UCR, and it wasn't until the late 1970s/early 1980s that enough police departments were using it to make the data reliable.
Something that you should know when interpreting police report data: it is susceptible to an issue that criminologists call the "dark figure of crime" -- which refers to all the crime that does not get reported to the police. Some types of crime are more susceptible to this dark figure of crime than others; for instance, hate crimes are notoriously susceptible because the people who are most likely to be targeted by hate crimes also tend to be the people who are least trusting of the police and are least likely to make a report. Thus, we only know the "true" prevalence of certain types of crime through the use of self-report data: that is, asking a representative sample of people (e.g. via a survey) if they have ever been a victim of crime. Some of these self-report surveys will also ask if the person then reported that crime to the police - so researchers have well-established the existence of under-reporting of certain types of crime (Pezzella et al., 2019).
Even though we have research going all the way back to the 1960s (for instance, Biderman & Reiss, 1967) that comments on the dark figure of crime, it was not until around the 1980s or so that criminologists/researchers consistently started using self-report data to cross-check police report data, and it also wasn't until around that time period that researchers were learning the right questions to ask to make sure that peoeple were properly self-reporting crime on surveys (Fisher et al., 2010). Thus, data from before the 1980s - and in many cases, data from the 1980s-1990s - is methodologically flawed, and requires careful thought to consider what the data is really saying.
The type of crime that has the lowest dark figure is homicide. In other words, homicide/missing people almost always get reported to the police. So, when researchers/scholars want to get the best estimate of a crime rate for a given period of time, given that the "dark figure" is so prevalent in almost every crime type, they look to homicide data - working off the assumption that homicides/missing people have mostly "always" been reported to the police, and police data has been used longer than self-report survey data.
I say all of this because your question has an underlying assumption that the number of serial killers/victims of serial killings spiking in the 70s-90s is "unique," or that there was something about that time period that created special opportunities for serial killers to thrive. The reality of the situation is that all crime was spiking at that time, and serial killers were no exception ... and it just so happens that the 70s-90s was a time period during which homicide data was the most widely used data for measuring overall crime rates, outside of certain academic circles where they were trying more innovative techniques using self-report data (and of course, the federal government was funding grants at that time to explore those innovative self-report techniques - Bonnie Fischer, who I cited earlier, was one such recipient of massive federal funding for her research into this issue with regards to sexual violence, like rape).